Former Time Inc. Chief Financial Officer Michael Klingensmith is a leading contender to become chief executive of the magazine giant, which is due to be spun out of Time Warner Inc. around the end of the year, say people familiar with the matter.

Mr. Klingensmith, 60 years old, is currently chief executive of Star Tribune Media Co. LLC, publisher of the Minneapolis Star Tribune. He left Time Inc. in 2008 after more than three decades...